Oh man, what a cool scenario. I can't say I have terribly much in the way to offer in terms of advice, as I've only played it once, as the U.S.A., and the player controlling the California/Texas conglomerate wasn't very experienced with the game, so his position collapsed fairly quickly and ended the scenario in a jiffy. But yeah, the C.S.A. player did seem to find himself a bit beleaguered independent of his compatriot's performance.
Are your Confederates getting rolled up at the local tactical level and can't hold their lines, or do you just feel that overall they don't have a winning strategy?
From an overall strategy perspective, the things I remember thinking might be weaknesses from the Union/Mexican side were the Panama Canal, New England, and Mexico itself. I can't remember the dynamics well enough to recall why taking Panama would have been valuable, but it seemed vulnerable. New England also felt pretty vulnerable, though invasions probably aren't easy. And Mexico, while not the crown jewel in terms of worthwhile cities to capture, has a lot of weak troops, so it felt vulnerable. As for defense, the South has a lot of mountains and good defensible terrain, but in the Midwest things are a bit trickier. If I recall correctly (unlikely), there's a city in the Midwest or in Oklahoma that seems really tough to defend from the get-go; it may be better to write off just to form a better line (though I could be wrong about that).
Anyways, good luck, and let us know what you come up with!